Our final exam will be **Monday, Dec 18** (at the usual class time, 10-11:40am).
The questions on the final exam will be very similar in format to the exercises on the Math Department’s Final Exam Review sheet:

MAT1275 Final Exam Review

(A hardcopy of the Final Exam Review sheet was handed out in class, and the pdf is also available online at http://www.citytech.cuny.edu/mathematics/docs/review/MAT1275FinalRview.pdf or on OpenLab: https://openlab.citytech.cuny.edu/groups/mat1275en-ganguli-fall2017/files/).

Note that many of the exercises on our midterm exams and quizzes were very similar in format to these exercises. The best way to review for the final is to **work through the Final Exam Review sheet, **and **study the related midterm exam solutions and quiz solutions **as you do so. All the midterm and quiz solutions are on OpenLab–download them!

Below is a guide to the exercises on the Final Exam Review sheet, with similar exam questions, WebWork exercises, and textbook examples listed for further review.

**#1: Solving Quadratic Equations (using the quadratic formula)**

- Quiz #3 (question #2)
- Quiz #4 (question #3)
- Exam #1 (question #3)
- WebWork: “QuadraticFormula” set

**#2: Graphing Quadratic Functions (by completing the square to identify the vertex)**

- “Graphing Quadratics” class handout (pdf available on OpenLab)
- Quiz #4
- Exam #2 (question #3)
- Exam #3 (question #1)

**#3: Simplifying Complex Fractions (using least common denominators)**

- Exam #2 (question #2)
- Exam #3 (question #6)
- WebWork: “ComplexFractions-Method1” set, Problem 6

**#4: Graphing Circles (by completing the squares to identify the center and radius)**

- Quiz #5 (question #1)
- Exam #2 (question #4)
- WebWork: “Circles” set, Problems 1-4

**#5: Complex Numbers (multiplying via “FOIL”; dividing using the complex conjugate)**

- Exam #2 (question #2)
- Quiz #8 (question #3)
- WebWork: “ComplexNumbers” set, Problems 5-8

**#6: Solving a system of 3 linear equations in 3 variables**

- Quiz #1
- Exam #1 (question #5)
- Algebra textbook, Sec 3.6: Example 1 (pp280-281)

**#7: Solving systems involving nonlinear equations**

- Exam #2 (question #5)
- Algebra textbook, Sec 9.4: Example 1(b) (p777), Example 4 (p779)

**#8: Finding the values of the trig functions based on the value of one trig function (and information about the sign of one other trig function):**

- Exam #3 (question #5)
- WebWork: “CoordinatePlaneTrig” set, Problems 4 & 5
- Trigonometry textbook, Sec 1.3: Example #5 (p26)

**#9: Using the Law of Sines or Law of Cosines**

- Exam #4 (TBD)
- Trig textbook, Sec 7.1: Example 1 (pp317-318)
- Sec 7.2: Examples 2 & 3 (pp331-332)

**#10: Verifying Trig Identities–use the fundamental trig identities and algebra**

- Exam #4 (TBD)
- Trig textbook, Sec 1.4: Examples 2-4 (pp32-33)
- Trig textbook, Sec 5.1: Examples 1 & 2 (pp212-213)

**#11: Solving Trig Equations (using the unit circle)**

- Exam #4 (TBD)
- Quiz #8 (question #2)
- WebWork: “SolvingTrigEquations” set (Problems 1-7)

**#12: Solving an exponential equation (using logarithms):**

- Exam #3 (question #3)
- Quiz #7 (question #1)
- Algebra textbook, Sec 8.7: Example 7 (p722)

**#13: Evaluating logarithms (using the definition of logarithms)**

- Exam #3 (question #2)
- Quiz #6 (questions #1(c) & #1(d))
- WebWork: “LogarithmicFunctions” (Problems 6-10)
- Algebra textbook, Sec 8.4: Examples 1 & 2 (pp682-683)

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